11.3 Homework Problems: Adding and Subtracting Rational Expressions
1. Find the equivalent numerator to make the rational expression valid
a. [latex]\frac{4x}{x-3}=\ \frac{}{\ \ \ \ \ \ \left(x-3\right)\left(x-9\right)\ \ \ \ \ \ \ \ \ \ }[/latex]
b. [latex]\frac{-6}{5x+6}=\ \frac{}{\ \ \ \ \ \ \ \ \ \ 25x+30\ \ \ \ \ \ \ \ \ \ \ \ \ }[/latex]
c. [latex]\frac{x+3}{x+8}=\ \frac{}{\ \ \ \ \ \ \ \ \ \ \left(x+8\right)\left(x-1\right)\ \ \ \ \ \ \ \ \ \ \ }[/latex]
2. Add the following rational expressions and simplify as much as possible
a. [latex]\frac{3x}{x+4}+\frac{12}{x+4}[/latex]
b. [latex]\frac{x-5}{x^2-2x+1}+\frac{x+3}{x^2-2x+1}[/latex]
c. [latex]\frac{5}{x-3}+\frac{x}{x^2-9}[/latex]
d. [latex]\frac{x+2}{3x+9}+\frac{2x-1}{2x-6}[/latex]
e. [latex]\frac{x-6}{7x^2-3x-4}+\frac{7-x}{7x^2+18x+8}[/latex]
f. [latex]\frac{3x+9}{x^2-5x+4}+\frac{49}{12+x-x^2}+\frac{3x+21}{x^2+2x-3}[/latex]
g. [latex]\frac{y^2-5y}{y+5}+\ \frac{7y-15}{y+5}[/latex]
h. [latex]\frac{x}{8}\ +\ \frac{5}{3}[/latex]
3. Subtract the following rational expressions and simplify as much as possible
a. [latex]\frac{2x+5}{2x^2-x-1}-\frac{4x+2}{2x^2-x-1}[/latex]
b. [latex]\frac{x^2+2}{x^2-4}-\frac{4x-2}{x^2-4}[/latex]
c. [latex]\frac{x}{x-1}-\frac{4}{x+2}[/latex]
d. [latex]\frac{3x}{6+x}-\frac{2x}{x^2-36}[/latex]
e. [latex]\frac{x-3}{4x^2-5x-6}-\frac{4x+10}{2x^2+x-10}[/latex]
f. [latex]\frac{d+4}{2d}-\ \frac{d-5}{7d}[/latex]
g. [latex]\frac{x+5}{x-4}-\ \frac{x-2}{x}[/latex]
4. Perform the requested operations and simplify as much as possible
a. [latex]\frac{x+1}{2x^2-x-1}+\frac{2x}{2x^2+5x+2}-\frac{2x}{3x^2+4x-4}[/latex]